@nqred: I did plug in x=\cos{ωt} and y=\sin{ωt} and got the right answer. Thanks.
@vanhees71: Your formula didn't parse because you used the wrong tags. You should use itex & /itex with [] enclosing them. Thank you for your help.
I still have one question. Is the potential energy V(r)...
The correct answer in polar coordinates that you refer to here is simply \mathcal{L}=\frac {m} {2}(\dot{r}^2). Right?
What I really want to ask is this: if a particle's Lagrangian in Cartesian coordinates is: \mathcal{L}=\frac{m}{2}(x^2+y^2) + \frac{mω^2}{2}(x^2+y^2) +...
I'm reading Leonard Susskind's The Theoretical Minimum Vol. 1.
1. The problem:
I'm on the section in which he asks the readers to derive the Lagrangian for a particle on a rotating carousel in polar coordinates.
2. Relevant ideas:
The same Lagrangian in Cartesian coordinates is given as...
If you refer to http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf you'll see that John Baez deduces the fact that granted the good old, F=ma it follows that there is some quantity whose critical points constitute the trajectory of a particle. And this quantity is what we...